1. Field of the Invention
The invention generally relates to electronics and in particular, to physical layer transceivers (including transmitter/receivers) with cascaded analog amplifiers.
2. Description of the Related Art
Many transceivers, such as a wireless radio frequency integrated circuit (RFIC), use multiple gain stages including open and closed loop amplifiers—each of which has multiple gain settings—to achieve an overall variable gain amplifier (VGA) with multiple gain settings.
Differential non-linearity (DNL) can be a problem with variable gain amplifiers. DNL refers to the deviation (from the ideal) in gain between two adjacent gain settings. The problem with DNL is typically most acute when more than one gain stage of a VGA is adjusted to switch between the two adjacent gain settings. For example, a particular gain stage can have a step size that is larger than the step size for the VGA as a whole, and when that gain stage is adjusted as part of a gain adjustment for the VGA, the DNL can be relatively high. When DNL is relatively high, gain adjustments can behave in unexpected ways, and can result in, for example, saturation of receiver stages, increases in bit error rates, etc.
It is desirable that the VGA as a whole has relatively small DNL in the total gain versus gain index curve. Absolute gain errors are usually not an issue because an automatic gain control (AGC) loop typically operates to establish the absolute gain of the system.
To illustrate, suppose the receiver or transmitter of a transceiver has two gain stages 602, 604 (FIG. 6) with gain G1 and G2, respectively. Each stage 602, 604 has multiple gain settings, as show below in Equation 1.
                                          G            1                    =                      {                                          g                11                            ,                              g                12                            ,                                                g                  13                                ⁢                                                                  ⁢                …                                      }                          ⁢                                  ⁢                              G            2                    =                      {                                          g                21                            ,                              g                22                            ,                              g                23                            ,                              g                24                            ,              …                        }                                              Equation        ⁢                                  ⁢        1            
Typically, one 602 of the gain stages with gain G1 in this example, has relatively few but relatively large gain steps, and the other stage 604, with gain G2 in this example, has relatively many but relatively small gain steps. Mathematically, the gain steps then observe the relationships expressed in Equation 2.
                                                        g                                                (                  1                  )                                ⁢                                  (                  x                  )                                                      -                          g                                                (                  1                  )                                ⁢                                  (                                      x                    -                    1                                    )                                                              >>                                    g                                                (                  2                  )                                ⁢                                  (                  y                  )                                                      -                                          g                                                      (                    2                    )                                    ⁢                                      (                                          y                      -                      1                                        )                                                              ⁢                              length                ⁡                                  (                                      G                    2                                    )                                                              >>                      length            ⁡                          (                              G                1                            )                                                            Equation          ⁢                                          ⁢          2                      ⁢        
When expressed as a logarithmic gain in decibels (dB), the total gain Gtotal with index n is as shown in Equation 3.Gtotal[n]=G1[ƒ1(n)]+G2[ƒ2(n)]  Equation 3
The functions ƒ1 and ƒ2 map the total gain index n to the gain required from each stage. Note that the index at which the larger step size gain stage 602 having gain G1 changes from lower to higher gain is referred to as index “B”. Note also that this is for purposes of illustration only and that the larger step size gain stage 602 with gain G1 can have any number of gain steps. The gain mapping can take the form illustrated with Equation 4.
                                                                        f                1                            ⁡                              (                n                )                                      =            1                    ;                      n            <            B                          ⁢                                  ⁢                                                            f                1                            ⁡                              (                n                )                                      =            2                    ;                      n            ≥            B                          ⁢                                  ⁢                                                            f                2                            ⁡                              (                n                )                                      =            n                    ;                      n            <            B                          ⁢                                  ⁢                                                            f                2                            ⁡                              (                n                )                                      =                          n              -                              (                                  B                  -                  1                                )                                              ;                      n            ≥            B                                              Equation        ⁢                                  ⁢        4            
To illustrate, consider the gain vectors in Equation 5.
                                          G            1                    =                                    {                              2                ,                14                            }                        ⁢            d            ⁢                                                  ⁢            B                          ⁢                                  ⁢                  G          2                =                              {                                          -                5                            ,                              -                4                            ,                              -                3                            ,                              …                ⁢                                                                  ⁢                10                            ,              11              ,              12                        }                    ⁢          d          ⁢                                          ⁢          B                                    Equation        ⁢                                  ⁢        5            
To achieve an overall linear gain, assuming that the gain step for the larger step size gain stage 602 with gain G1 occurs at B=11, the gain mapping functions can be as shown in Equation 6.
                                                                        f                1                            ⁡                              (                n                )                                      =            1                    ;                      n            <            11                          ⁢                                  ⁢                                                            f                1                            ⁡                              (                n                )                                      =            2                    ;                      n            ≥            11                          ⁢                                  ⁢                                                            f                2                            ⁡                              (                n                )                                      =            n                    ;                      n            <            11                          ⁢                                  ⁢                                                            f                2                            ⁡                              (                n                )                                      =                          n              -                              (                                  11                  -                  1                                )                                              ;                      n            ≥            11                                              Equation        ⁢                                  ⁢        6            
An example of the individual gain characteristics of each gain stage 602, 604 having gains G1 and G2, respectively, and the total gain Gtotal versus the gain index is shown in FIG. 1. In FIG. 1, gain is expressed along the vertical axis and the index is expressed along the horizontal axis. FIG. 1, labeled as “prior art,” represents the ideal case, which is rarely achieved due to process, voltage, and temperature variations.
FIG. 4 illustrates an example of a gain profile in which the open loop RF gain step for the larger step size gain stage 602 has some gain imprecision.